Quite recently, there have been considerable progresses on the bounds of various quantum channel capacities for bosonic Gaussian channels. Especially, several upper bounds on the classical capacity and the quantum capacity on the bosonic Gaussian channels, via a technique known as a quantum entropy power inequality, have been shed light on understanding the mysterious quantum-channel-capacity problems. However, upper bounds for the private capacity on quantum channels are still waiting for the study on certain universal upper bounds. Here, we derive upper bounds on the private capacity for bosonic Gaussian channels involving a general Gaussian-noise case through the conditional quantum entropy power inequality.

中文翻译：

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玻色高斯通道的私有容量上限

最近，玻色高斯通道的各种量子通道容量的界限取得了相当大的进展。特别是，经典容量和玻色高斯通道上的量子容量的几个上限，通过一种称为量子熵功率不等式的技术，已经阐明了理解神秘的量子通道容量问题。然而，量子信道上私有容量的上限仍在等待某些通用上限的研究。在这里，我们通过条件量子熵功率不等式推导出涉及一般高斯噪声情况的玻色高斯通道的私有容量的上限。